GATE Civil Engineering
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The state of $2D$-stress at a point is given by the following matrix of stresses:

$$\begin{bmatrix} \sigma_{xx} & \sigma_{xy} \\ \sigma_{xy} & \sigma_{yy} \end{bmatrix} = \begin{bmatrix} 100 & 30 \\ 30 & 20 \end{bmatrix} MPa$$

What is the magnitude of the maximum shear stress in MPa

  1. $50$
  2. $75$
  3. $100$
  4. $110$
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